To find the volume of the cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is a constant approximately equal to 3.14.
Given:
- The radius \( r = 12 \) feet,
- The height \( h \) is half the length of the radius, so \( h = \frac{1}{2} \times 12 = 6 \) feet.
Now, plug these values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (12)^2 \times 6 \]
Calculating \( (12)^2 \):
\[ (12)^2 = 144 \]
Now substitute this into the volume equation:
\[ V = \frac{1}{3} \times 3.14 \times 144 \times 6 \]
Calculating \( 144 \times 6 \):
\[ 144 \times 6 = 864 \]
Now we substitute this into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 864 \]
Next, calculate \( \frac{1}{3} \times 864 \):
\[ \frac{1}{3} \times 864 = 288 \]
Finally, multiply \( 288 \) by \( 3.14 \):
\[ V = 288 \times 3.14 = 904.32 \]
Now, rounding to the nearest tenth, we find:
\[ V \approx 904.3 \]
Thus, the volume of Erik’s cone is approximately 904.3 cubic feet.